Lunch time at my daughter’s small school means children are free to move around both inside and outside of the school within boundaries determined by their grade level. Often, lunch time is not just for eating (as evidenced by half-eaten sandwiches in the lunch box at the end of the day).  Lunch is for making up skits, finding interesting properties in the rocks you are pounding, for having arguments and making up, for exploring the narrow (but long) strip of trees that line one side of the school’s property, called ‘the woods’, and for creating clubs.  At a school with a no-exclusion rule, a club can be pretty much any combination of kids at any one time.

One day, when my daughter was in third grade, she told me her club had made a fort in the woods. At first glance it looked rather like a wall.  A very well constructed, sturdy wall, a wall built with a lot of thought and insight. There is a base of bricks and concrete and then a layer of sticks. There was also a latch (a piece of wire) which is lifted by the “door” (a stick), “Although we don’t usually go in this way because it’s not sturdy,” she told me, “we usually just go in over the low wall.”

Hearing about and seeing this fort I immediately thought about the article Ophelia’s Fort by fourth grade teacher and artist David Rufo which I edited for the Teaching Artist Journal’s online writing community ALT/space. In it he writes:

“During our conversations it became evident that Ophelia was focused on making for herself a “special place” rather than a special structure with four walls, a roof, and a door. As David Sobel emphasized in his book Children’s Special Places: Exploring the Role of Forts, Dens, and Bush Houses in Middle Childhood: ‘Through making special places, children are experiencing themselves as shapers and makers of small worlds. This experience contributes to making them active shapers of the world in their adult lives.'”

 In sharing this story about my daughter’s lunchtime adventures, I am aware that it is not about math learning, per se, but it does relate to why I wrote a book about the whole-body math learning. In past writings I have focused very closely in on the specifics of the Math in Your Feet program; the new book was a chance for me to step back and look at the broader issues involved in making math and dance at the same time.

One of the ideas that came into view as I zoomed out during the book writing is the necessity of agency in learning. It is clear that issues of learner agency begin with the body.  And, when thinking about using dance or movement as a partner in learning we must start by identifying how the body has historically been employed during school hours.  That is to say, how the body has not been employed (bolding emphasis mine):

“The embodied experience of traditional schooling is often, as educational philosopher John Dewey might suggest, an anaesthetic experience, devoid of any heightened sensory experience or perception. In school, our bodies are still, serving primarily a utilitarian function.  We learn to from an early age not to squirm or leave our desk chairs in classrooms. We learn to sit up straight, raise our hands to be called upon, or walk single file to lunch.  By the time we reach high school our bodies are often reserved for gym class…or for moving from one class to another. In a sense, we educate from the neck up, leaving the rest of the body to act largely as physical support rather than as actively involved in our quest for knowledge, thinking, and understanding … implicated in this analysis is the importance of agency in relation to activity. Providing curricular opportunities that are experience-based, that encourage the use of the body and engage the senses in learning could create a different kind of [structure] for schooling if learners are encouraged to explore connections between learning, self and the broader social and cultural frameworks of meaning in which they are situated.” 

Source: Powell, K. The apprenticeship of embodied knowledge in a taiko drumming ensemble. In L. Bresler (Ed.), Knowing bodies, moving minds: Embodied knowledge in education (pp. 183-195). Dordrecht, The Netherlands: Klewar Press.

The body is not simply a vehicle toward realizing the perceived pinnacle of abstracted knowledge housed in the mind.  The body is where learning originates. Living in a body is also the way children learn personal agency as they make decisions about how their bodies will move and act and how that power can influence and shape their world. And, in the process, learning that there are obvious consequences and responses in relation to their actions. This is literally and viscerally democracy in action.

Perhaps most importantly, despite the incredible change of pace and screen-focused activity in modern life, children still have brains that learn best by moving and pulling sensory input in through all parts of the body.  Hundreds of years of thoughtful analysis, research, and observation of children learning and growing has shown this to be true and yet the body is still being marginalized in favor of  “knowledge” as something gold and shiny to be won and placed on a high shelf for viewing, far removed from any experience and personal understanding.

What is a body without agency?  What is learning without a body? Thinking about these questions is the important first step in understanding the inherent worth of children using their bodies to make sense of mathematics.

This is slightly altered reposting of the 2013 version of the same title on the authors former blog The Map is Not the Territory.

Malke Rosenfeld is a dance teaching artist, author, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Her new book is titled: Math on the Move: Engaging Students in Whole Body Learning (Heinemann 2016)

Math on the Move: Engaging Students in Whole Body Learning is organized around three basic ideas:

1. The body in math learning is best conceived as a thinking tool
2. Math learning is more than memorization
3. Amazing learning can happen when the body and math come together in both dance and non-dance settings.

It’s point #2 I’d like to focus on in this post.

A couple years ago Ben Orlin had a fantastic article in the Atlantic titled When Memorization Gets in the Way of Learning. In it, he says:

“What separates memorization from learning is a sense of meaning. When you memorize a fact, it’s arbitrary, interchangeable–it makes no difference to you whether sine of π/2 is one, zero, or a million. But when you learn a fact, it’s bound to others by a web of logic. It could be no other way.”

Most often, the role of the moving body in the classroom, during math time, is that of mnemonic device. Here are some examples of what that might look like:

• using arms to create symbols for operations, like +, – , and = (focusing on creating representations of the symbols, not expressing their meaning)
• using hand movements in a song about memorizing a procedure
• bouncing on an exercise ball while reciting multiplication facts
• singing a song with an accompanying dance about finding the area of a circle, using movements that bear no relationship to the properties of a circle
• exploring a math concept such as high versus low in isolation, removed from a narrative context (such as retelling a story) or the larger context of dance learning and making
• having multiple students become the sides of a triangle by lying on the floor

None of these activities are inherently harmful, some of them may be helpful, and yet, none are at all focused on making sense of mathematical ideas.

In the book I endeavor to explain why we should use the whole, moving body in math learning. I do this by pulling from both research and practice to build a framework for meaningful, body-based math learning. When children harness their innate body knowledge for mathematical sense making, they also harness their whole selves in the pursuit of new ideas and understanding. They develop, communicate, and reason about mathematical ideas both nonverbally and verbally.

Children can make good sense of the world when they get a chance to interact with it, and children are also well able to reason with and about things they observe and do. But they can do this only if they get the chance to do, make, investigate, converse, wonder, build, express, and reflect. Without these kinds of interactions they might still be able to memorize math facts, but memorization would not necessarily mean they would know, for themselves, that something was true.

Ben Orlin said it best:

“Memorization is a frontage road: It runs parallel to the best parts of learning, never intersecting. It’s a detour around all the action, a way of knowing without learning, of answering without understanding.”

I’m SO looking forward to the book being out in another month or so we can grow the practice of meaningful whole-body math learning and teaching together. In the mean time, please feel free to join our book group on Facebook, comprised of educators who want to help their students make sense of math using the original “object to think with” — the whole, moving body.

Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in October 2016.